Champagne wrote:Nice findings with theses starts, but I would like to share some experiences and perplexity.In tarx0075, first assigned following Allan model is 2r6c2.I introduced it as given and processed the puzzle in my standard way.Results were [worse] than without that given. Likely this new given opened new doors, but did not simplify the main path.

I agree, and I think this is also true for most methods. For the really difficult puzzles, these loops are just a small appetizer, they may not help solve the puzzle at all.

Champagne wrote:..... these 2 eliminations don't come in the first ten of my process.

This is the only significant difference I see, these loop-like structures often come first when searching for base/cover set elimination logic. I don't know why.

Champagne wrote:.It seems that both ways (Allan Model and AIC's nets) are fighting against completely different weaknesses of the puzzle.

Maybe this is also becasue one is base/cover set based, and another is AIC based?

Only two sets for digts '1' and '4'. The corresponding diagram should be relatively easy to analyze

Thanks for the reply, but I can't find anything useful in there.

Are all the Xs above representing base sets (Allan,s sets) or a mix of base sets and cover sets (linksets)

For the N row, is the digit 6 shown at the bottom the row number or the column number?

Also, I find your format much less user friendly than Allan's format of {1R6 3R24568 4R7 5R1269 7R24568}, e.g., for the R row Xs above. Counting over the dots is relatively error prone and not much fun.

Only two sets for digts '1' and '4'. The corresponding diagram should be relatively easy to analyze

Thanks for the reply, but I can't find anything useful in there.

Are all the Xs above representing base sets (Allan,s sets) or a mix of base sets and cover sets (linksets)

For the N row, is the digit 6 shown at the bottom the row number or the column number?

Also, I find your format much less user friendly than Allan's format of {1R6 3R24568 4R7 5R1269 7R24568}, e.g., for the R row Xs above. Counting over the dots is relatively error prone and not much fun.

In my country we say" the nicest girl can't give more that what she has".

Regarding Allan model, Allan does more than my solver. He has specific tools and a process I could not fully copy up to now.

I can clarify small points:

1) This format is the format agreed with Allan to show a mixed set/linkset group. At that point, there is still some work to do to come to a SLG ; spliit of the "sets" in a Set/Linkset form and normally reshaping slightly the diagram to come to the "nicest form".

2) As such, it proves the elimination (here 4r7c2), so it is normally possible to use it to find alternative way to express the same logic.I did it for other situations.

Following Champagne's logic above, I was looking more closely at Golden Nugget morphs, I was surprised to find a loop identical to the inital loop from tarek-0075. These loops are similar to ones found in other puzzles notably Fata Morgana. The Golden Nugget loop is also 4 layers.

I have placed most the data in the Great Monster Loops thread, including grids and a logic diagrams, including for Fata Morgana. It looks like FM only differs because it is missing the top layer (relative to the diagram) of the other two puzzles.

Looking more closely at Golden Nugget morphs, I was surprised to find a loop identical to the inital loop from tarek-0075. These loops are similar to ones found in other puzzles notably Fata Morgana. The Golden Nugget loop is also 4 layers.

Hi Allan,

Happy to see you again,

I came to the same conclusion as explained some posts above, and I have other examples.

All these puzzle have in common the same property, first seen in Fata Morgana:

some cells (usualy 2, but it can work with more) having a limited number of "free" digits (3 in Fata Morgana, 4 for other examples in your list) 2 of them needed in the solution are such that

If a digit is True in those cells then one at least of two other cells is True as well.

As a matter of fact, these two cells have the same super candidate as the original.

I am working on designing a derived use of your model to find specifically that pattern and include it in the AIC process.

champagne

BTW, you disclose a new loop for the start of Golden Nugget. I used above the loop copied form your website some days ago.

champagne wrote:I came to the same conclusion as explained some posts above, and I have other examples.

Yes, I saw, my post was in support of your's. I added a brief note to mine to clarify.

champagne wrote:BTW, you disclose a new loop for the start of Golden Nugget. I used above the loop copied form your website some days ago.

It is basically the same loop. I used the same old logic, which I called a layer cake, and morphed it to something like tarek-0075. My software then eliminated the need for the set in digit level 6, producing the tarek-0075 look-a-like loop. I think your logical arguments must apply either way.

I have found an easy way to work with these (Champagne) diagrams, with the help of a new feature, and this diagram makes a good example. It works this way.

1. Paste the Champagne diagram, I will see the 39 sets, no elimination, yet.2. I then "Autofill Cover Sets" to find the eliminations. This finds a minimum set of linksets needed to make the eliminations.3. Optionally, I can then convert (base) sets to linksets to make a standard SLG.

This process assumes that the 39 sets include all base sets required for elimination, in other words, it assumes the only missing sets are weak linksets. For this examples I get: